Some results on a conjecture regarding Mori domain

Abstract

Based on the famous Mori-Nagata Theorem: The integral closure of a noetherian domain is a Krull domain, similar assertion was conjectured for Mori domain as follows: The complete integral closure of a Mori domain is a Krull domain. The conjecture is positive for a noetherian domain, Krull domain, a semi normal Mori domain [6] and Mori domains for which (D : D*) ≠ 0. In general, as M. Roitman has noted [26], the conjecture is not true. In this paper, an attempt is being made, among other things, to prove that the conjecture is true for a one dimensional Mori domain and for a finite dimensional AV- Mori domain. On the other hand, using the idea of conductor ideals, a simplified proof is given that the conjecture is true for semi normal Mori domains with nonzero pseudo radical.